Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26011395 | C2 | semidirect |
| 3. #26011382 | C2 | semidirect |
| 4. #26011381 | C2 | semidirect |
| 6. #26011362 | C2 | semidirect |
| 7. #26011359 | C2 | semidirect |
| 8. C4×#14583803 | C2 | semidirect |
| 9. C4×C4⋊C4×C173 | C2 | semidirect |
| 13. #19149667 | C4 | semidirect |
| 34. C2×Dic346 | C2×C4 | semidirect |
| 47. #14583803 | C2×C4 | semidirect |
| 48. #14583803 | C2×C4 | semidirect |
| 58. C42×C173 | C2×C4 | semidirect |
| 118. C173 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D173 | semidirect |
| 177. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| #26011395 | 2 |
| #26011382 | 2 |
| #26011381 | 2 |
| #26011369 | 2 |
| #26011362 | 2 |
| #26011359 | 2 |
| C4×#14583803 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #2337 | 173 |